Problem: Kevin is 2 times as old as Daniel. Eighteen years ago, Kevin was 8 times as old as Daniel. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Daniel. Let Kevin's current age be $k$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $k = 2d$ Eighteen years ago, Kevin was $k - 18$ years old, and Daniel was $d - 18$ years old. The information in the second sentence can be expressed in the following equation: $k - 18 = 8(d - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = 2d$ . Substituting this into our second equation, we get: $2d$ $-$ $18 = 8(d - 18)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $2 d - 18 = 8 d - 144$ Solving for $d$ , we get: $6 d = 126.$ $d = 21$.